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When cross and dot product equal what is angle between A and B?
Wiki User
∙ 11y ago
A · B = |A| |B| cos(Θ)
A x B = |A| |B| sin(Θ)
If [ A · B = A x B ] then cos(Θ) = sin(Θ).
Θ = 45°
Wiki User
∙ 11y ago
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When does the magnitude of dot product and cross product of vectors is equal?
If x is the angle between the two vectors then the magnitudes are equal if cos(x) = sin(x). That is, when x = pi/4 radians.
What is the difference between the ''dot product'' and the ''cross product''?
Dot Product:Given two vectors, a and b, their dot product, represented as a ● b, is equal to their magnitudes multiplied by the cosine of the angle between them, θ, and is a scalar value.a ● b = ║a║║b║cos(θ)Cross Product:Given two vectors, a and b, their cross product, which is a vector, is represented as a X b and is equal to their magnitudes multiplied by the sine of the angle between them, θ, and then multiplied by a unit vector, n, which points perpendicularly away, via the right-hand rule, from the plane that a and b define.a X b = ║a║║b║sin(θ)n
What is the difference between a 'dot product' and a 'cross product'?
Dot Product:Given two vectors, a and b, their dot product, represented as a ● b, is equal to their magnitudes multiplied by the cosine of the angle between them, θ, and is a scalar value.a ● b = ║a║║b║cos(θ)Cross Product:Given two vectors, a and b, their cross product, which is a vector, is represented as a X b and is equal to their magnitudes multiplied by the sine of the angle between them, θ, and then multiplied by a unit vector, n, which points perpendicularly away, via the right-hand rule, from the plane that a and bdefine.a X b= ║a║║b║sin(θ)n
Dot product of two vectors is equal to cross product what will be angle between them?
(A1) The dot product of two vectors is a scalar and the cross product is a vector? ================================== (A2) The cross product of two vectors, A and B, would be [a*b*sin(alpha)]C, where a = |A|; b = |B|; c = |C|; and C is vector that is orthogonal to A and B and oriented according to the right-hand rule (see the related link). The dot product of the two vectors, A and B, would be [a*b*cos(alpha)]. For [a*b*sin(alpha)]C to equal to [a*b*cos(alpha)], we have to have a trivial solution -- alpha = 0 and either a or b be zero, so that both expressions are zeroes but equal. ================================== Of course one is the number zero( scalar), and one is the zero vector. It is a small difference but worth mentioning. That is is to say if a or b is the zero vector, then a dot b must equal zero as a scalar. And similarly the cross product of any vector and the zero vector is the zero vector. (A3) The magnitude of the dot product is equal to the magnitude of the cross product when the angle between the vectors is 45 degrees.
Can a proportion be equal if the cross products are not equal?
No. A cross product is just a way of simplifying a proportion. If the cross product aren't equal, it follows logically that the proportion isn't equal.
What is the angle in which the dot product of two non zero vectors is equal?
It depends on what the dot product is meant to be equal to.
What is the relation between angle of friction and angle of repose?
Angle of repose is equal to angle of friction.
What is the possibility when magnitudes of dot and cross products are equal?
if any one of the vectors is a null vector or if A is the angle between the two vectors then tanA =1
Can the vector product of two vectors be negative?
no .....the scalar product of two vectors never be negative Yes it can If A is a vector, and B = -A, then A.B = -A2 which is negative. Always negative when the angle is between the vectors is obtuse.
How do you find out how to write the ratio for sin X cos X and tan X in a right triangle?
For sinX you set it equal to the opposite side of the angle over the hypotenuse(SOH),cross multiply. CosX you set it equal to the adjacent side of the angle over the hypotenuse (CAH), cross multiply. Lastly for TanX set it equal to the opposite of the angle over the adjacent side of the angle and then cross multiply (TOA). I hope that's helpful :)
When two vectors are added and their magnitude is equal to the magnitude of resultan what will be angle in between them?
if you add the vectors magnitude and equal to resultant the angle between them is 0
What is the relationship between angle of incindence and angle of reflection?
Both angles are equal.
